Approximation of Non-Analytic Functions by Analytical Ones
We study the properties of the elements of best approximation for functions defined in the unit disk by functions from the Bergman space. For functions of a special type, we find a sufficiently accurate description of the properties of these elements in terms of the Hardy and Lipschitz classes. The obtained result is based on an analysis of the corresponding duality relation for extremal problems. The developed method is also applicable to relatively smooth (in terms of Sobolev spaces) approximated functions.
Key wordsBergman space Hardy space best approximation linear functional extremal problem
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Supported by Russian Foundation for Basic Research, grant No. 18-01-00017.
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